Novikov operad is not Koszul

TL;DR

This paper proves that the Novikov operad, defined by specific algebraic identities, does not possess the Koszul property, impacting the understanding of its algebraic structure.

Contribution

It establishes that the Novikov operad is not Koszul, providing a significant insight into its algebraic properties and structure.

Findings

Novikov operad is not Koszul

Provides proof of non-Koszul property for Novikov operad

Clarifies the algebraic nature of Novikov operads

Abstract

An algebra with identities $a\circ(b\circ c-c\circ b)=(a\circ b)\circ c-(a\circ c)\circ b$ and $a\circ(b\circ c)=b\circ(a\circ c)$ is called Novikov. We show that Novikov operad is not Koszul.